Substitute means to put in place of another. In algebra, substitution can be used to replace variables with values, terms, or expressions.

Elimination is a technique to help solve equations simultaneously and is where one of the variables in a problem is removed.

Problem solving with linear and quadratic simultaneous equations

Maths

Checking and securing understanding of interpreting graphs

Forming simultaneous equations

Combining equations

Solving simultaneous equations by elimination from a context

Solving algebraic simultaneous equations by elimination

Solving more complex simultaneous equations by elimination

Solving simultaneous linear equations by substitution

Solving simultaneous linear equations graphically

Solving a quadratic and linear pair of simultaneous equations using elimination

Solving a quadratic and linear pair of simultaneous equations using substitution

Solving a quadratic and linear pair of simultaneous equations graphically

Solving simultaneous equations via any method

In the future unit, pupils will learn how to extend their understanding of solving equations and extend this to consider inequalities. Pupils will consider a variety of inequalities and ways that their solutions can be represented.

In the prior unit, pupils learnt to solve quadratic equations by factorising and this skill will be required in this unit through manipulating two simultaneous equations to find the solutions. For pupils studying the higher content, solving quadratic equations is required if one of the simultaneous equations is a quadratic.

In this unit pupils will learn to solve a pair of simultaneous equations from different starting points and cases using a variety of strategies.

Simultaneous equations: 2 variables

4 red and 5 blue boxes weigh 33g. 7 red and 2 blue weigh 24g. What is the mass of each box?

7 red and 5 blue boxes weigh 86g. 5 red and 7 blue weigh 82g. What is the mass of each box?

3 small & 5 large toys cost £185. 5 small & 3 large cost £175. What is the cost of each toy?

Using 4 hours of light A and 6 hours of light B consumes 240 watts. If 6 hours of A and 4 hours of B are used instead, it consumes 280 watts. What is the power consumption per hour for each light?

A publisher prints novels and textbooks. Printing 4 novels and 6 textbooks costs £320. Printing 6 novels and 4 textbooks costs £280. What is the printing cost for each type of book?

A café blends 3 kg of Brazilian beans (B) with 2 kg Columbian (C) to create a blend for £50. Another blend mixes 2 kg from B with 3 kg from C for £60. What is each bean price per kg?

Which equation is true for $$x = 2$$ and $$y = 5$$? 

If I add together the pair of simultaneous equations $$7x + 7y = 87$$ and $$5x + 7y = 91$$, what is the resulting equation? 

Multiply this equation by $$5$$: $$3x + 10 = 40$$

What is the value of $$x$$ for equations $$6x + 8y = 66$$ and $$x + 3y = 16$$?

What is the negative coordinate pair that solves both $$x^2 + y^2 = 40$$ and $$x - y = 4$$?

What is the negative coordinate pair that solves both $$x^2 + y^2 = 17$$ and $$x - y = 3$$?

Problem solving with linear and quadratic simultaneous equations

Lesson outcome